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Journal Articles Numerische Mathematik Year : 2017

A finite volume scheme for boundary-driven convection-diffusion equations with relative entropy structure

Abstract

We propose a finite volume scheme for a class of nonlinear parabolic equations endowed with non-homogeneous Dirichlet boundary conditions and which admit relative en-tropy functionals. For this kind of models including porous media equations, Fokker-Planck equations for plasma physics or dumbbell models for polymer flows, it has been proved that the transient solution converges to a steady-state when time goes to infinity. The present scheme is built from a discretization of the steady equation and preserves steady-states and natural Lyapunov functionals which provide a satisfying long-time behavior. After proving well-posedness, stability, exponential return to equilibrium and convergence, we present several numerical results which confirm the accuracy and underline the efficiency to preserve large-time asymptotic.
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Dates and versions

hal-01326029 , version 1 (03-06-2016)
hal-01326029 , version 2 (05-07-2016)
hal-01326029 , version 3 (02-02-2017)
hal-01326029 , version 4 (19-04-2017)

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Cite

Francis Filbet, Maxime Herda. A finite volume scheme for boundary-driven convection-diffusion equations with relative entropy structure. Numerische Mathematik, 2017. ⟨hal-01326029v4⟩
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